I am analyzing data in order to develop a model for power generation of a solar system based on three predictor variables. I have done t-tests showing significant improvement in the generation while varying one variable at a time. Each variable has only two possible values in my situation, and for each variable I have a 95% confidence interval on the change in generation.
While it is great to understand the effect of each variable alone, I would like to somehow develop a model that can predict the change in generation given the affects of multiple variables.
I'll write this out symbolically if that helps explain my situation.
Three predictor variables A B C
Each has two possible values, 1 or 0.
My response variable is G
I know how G changes when I vary A whilst B and C are held constant. I know the same for when I vary B and C (holding the other two constant).
I would like to know how G changes when I vary more than one of A, B, or C.
What sort of statistical process would I use to create such a model?
Comment to rolando2:
After reading your article, I am not quite sure that i'm working with interactions. Let me put numbers to what I have right now to make this more concrete.
One of the predictor variables is angle. I know that when changing the angle from 15 to 30 degrees, everything else being constant, I generate 80 more watts on average. This I found using a paired 2-sample t-test with daily data over a year for both angles side-by-side.
Another variable is inverter type. I know that when I use inverter B instead of inverter A, I produce 40 more watts on average.
I am guessing that if we put together a system with 30 degree tilt and inverter B, and compare that to our "standard" system with 15 degree tilt and inverter A, we would not generate 120 more watts on average.
How would I know how much more I would produce without having to experimentally test each combination?
P.S. My experience in multivariable statistics is very limited, as you probably might have guessed. I have a semester course of statistics based in R, following a year of AP Stats in HS.